1. Field of the Invention
The present invention relates to communication systems and, in particular, to receivers that use channel shortening methods.
2. Description of the Related Art
Transmissions in modern digital communication systems are made up of data bursts or pulses defined by a well-known modulation scheme and sent through a channel. In an ideal transmission channel there is only a pure delay affecting each pulse and there is no interference between pulses. The signal received from an ideal channel is a delayed replica of the transmitted signal. In reality, and most adversely in wireless channels, there are a number of delay paths in the channel and the delays may be time varying. These delays cause inter-symbol interference (ISI) that degrades transmission and reduces achievable bit rates. Therefore, prior to demodulation at the receiver, the receiver typically calculates a filter and applies that filter to correct the ISI degradation prior to demodulation.
A filter that controls the amount of ISI between symbols in multi-carrier modulated signals is usually termed a channel-shortening filter (CSF). A filter can be designed from statistical measures of the received signal to shorten the delay spread of the channel. Depending on channel characteristics, the filter can be designed to simultaneously suppress interference sources. It can be said that the CSF shortens the total time dispersion over which the channel has its maximum delay spread.
Multi-carrier modulation (MCM) techniques such as orthogonal frequency division modulation (OFDM) are gaining wider application in wireless and wireline communication systems. MCM systems benefit from channel shortening filters to restrain ISI dispersion to within a pre-determined time guardband defined by the system. Since the time guardband contains the initial symbol samples, it is termed the cycle prefix (CP). OFDM with a channel-shortening CP filter (CSF) has been incorporated into a variety of standards like DSL, WiMax (802.16), WiFi (802.11), digital video broadcast (DVB), digital audio broadcast (DAB) and personal area networks (802.15). The time guardband between symbols allows a CSF to mitigate time channel dispersion without requiring a receive filter to remove all time dispersions. In DSL applications, the CSF is given the name of a time equalizer (TEQ).
Recent OFDM applications insert a long time guardband between symbols to reduce the need for a TEQ at the receiver. The assumption made is that the TEQ is unnecessary if a time guardband greater than the maximum (significant) delay is used. This time guardband drops the achievable bit rate by increasing the symbol duration but allows use of a simplified receiver. Conventional CSF/TEQ calculations are computationally intensive.
In some applications, it is preferable to include a TEQ. In DSL applications, for example, the channel dispersion has delayed paths of significant power that make the use of an adequate time guardband impractical. Therefore, DSL is typically implemented with a TEQ. Wi-Fi (IEEE 802.11) and WiMax (IEEE 802.16) allocate a time guardband to mitigate the time dispersions expected in the channel, which necessarily reduces the system throughput. The nature of wireless cellular networks is such that interference from other sources and adjacent cells also lower operational bit rates. In wireless systems, the time dispersions and interferences are time-varying depending on the receiver's speed of motion, which is not found in DSL systems. So time guardbands are only moderately effective in optimizing the performance of these, and other, wireless transmission systems.
Multi-carrier modulation is not the only communication system benefiting from a CSF. A maximum likelihood sequential estimation (MLSE) receiver is the optimum receiver in many communication systems. The complexity of an MLSE receiver grows exponentially with the number of coefficients in the channel. Therefore, a CSF is chosen to control receiver complexity by shortening the channel to a target delay spread value and to provide the new overall channel response for MLSE calculations. In multi-user detection (MUD) systems with flat-fading channels, the application of a CSF also reduces the optimum receiver complexity.
A performance issue with channel shortening filters is that the resulting channel of the transmission channel convolved with the CSF response has an impulse response extending to the target delay spread. This overall response, called the target impulse response (TIR), can affect performance. Therefore, a CSF Design 146 method typically determines a TIR that will maximize a performance criterion.
DSL systems typically require two equalizers, one for the time domain equalization (TEQ) to shorten the channel, and another for per-frequency corrections in amplitude and phase called a frequency equalizer (FEQ). The TIR determines the FEQ design.
Conventional communication systems, like those illustrated in FIG. 1, determine the CSF filter in “one-shot.” That is, the receiver determines a single filter to simultaneously satisfy the TIR and the target delay spread criteria. Referring to FIG. 1, a modulator 120 modulates the information bits 110 in accordance with the chosen waveform. The channel 130 represents all the interference, noise and ISI incurred in the transmission of the modulated signal as seen by the CSF 142. Channel 130 is modeled to include the actual channel dispersion, the receiver's analog front-end filter and any pulse shaping filter at the transmitter used to control the modulated signal's bandwidth. Quantization noise and analog front-end amplifier noise are the two usual noise sources included in the model. In DSL and wireless applications, there will also be interference sources from other telephone lines or cell sites. The CSF 142 provides an overall impulse response to the demodulator 144 that is designed to not exceed a target delay and to maximize a performance criterion. The CSF Design 146 calculates the required statistics and signal decomposition necessary to achieve the filter performance goals (i.e., meeting TIR and delay spread constraints).
Researchers have developed computationally efficient approaches to calculate the filter coefficients in the CSF Design 146. Generally, the algorithms for CSF Design 146 are based on the measured properties of the received signal and use linear algebra techniques to calculate the filter coefficients. For this reason, the CSF 142 is most typically a finite impulse response (FIR) filter.
The CSF Design 146 in FIG. 1 involves a number of steps and optimizations. The process includes:
1. Select a performance criterion
2. Estimate channel 130 coefficients
3. Calculate a TIR
4. Calculate the CSF 142 for a given delay Δi 
5. Repeat steps 3 and 4 for a next possible delay i+1
6. Select optimum CSF over all delays
The CSF 142 can be designed to optimize one of various performance criteria. In the case of OFDM, the optimization criterion may be dependent on the communication system. In DSL applications, the optimization is related to the achievable bit rate. Wireless applications seek to optimize SINR, which can be represented via a number of performance criteria. The maximum shortening SNR (MSSNR), which maximizes the ratio of the energy in the admissible delay spread (i.e., the TIR time span) to the energy outside that interval, is one such an SINR maximization criterion. Another criterion to maximize SINR is the traditional minimum mean square error (MMSE) criterion. In the case of an additive white Gaussian channel, the MMSE and MSSNR criteria determine the same CSF.
CSF Design 146 methods conventionally require knowledge of the channel coefficients to estimate the CSF 142. FIG. 2 shows how most conventional CSF Design 146 methods accomplish the filter design. The model uses knowledge of the channel coefficients 210 to determine a TIR 224 and, given a choice of a particular delay 222, to calculate the resulting CSF 220. Therefore, the first step is to estimate the channel coefficients over a sufficiently long delay spread. Various methods can be implemented to estimate the channel coefficients from the training symbols or pilot tones, depending on the signal of interest.
For the MMSE criterion, the TIR 224 is calculated as the eigenvector corresponding to the smallest eigenvalue of a delay-dependent auto-covariance matrix. This delay-dependent matrix involves the calculation of the inverse of the auto-covariance matrix for the received signal. Calculation of this matrix inverse is very computationally expensive for each delay; hence the MSSNR criterion typically provides lower complexity.
For either the MMSE or the MSSNR criterion, the generalized eigenvalue system is solved for each delay to obtain the desired TIR 224, which is preferably the optimum TIR, and subsequently, the CSF 220.
Subsequent to the TIR calculation, the MMSE CSF is calculated for a specific delay Δi by solving a generalized eigenvector problem with auto-covariance and cross-covariance matrices. These covariance matrices are calculated by averaging the prescribed products of the received signal and the training sequence or sequences. While determining the TIR requires a search for the eigenvector associated with the minimum eigenvalue of a delay-dependent auto-covariance matrix, the CSF is calculated by solving a generalized eigenvector equation involving the auto- and cross-covariance matrices. This calculation is repeated for each delay, since the TIR is a variable in the generalized eigenvector equation.
In the case of the MSSNR criterion, a generalized eigenvector equation is solved to determine the CSF. That is, the eigenvector corresponding to the smallest eigenvalue must be estimated for each possible delay. The generalized eigenvector equation contains two matrices completely constructed from the known, or estimated, channel coefficients. Unlike the MMSE criterion, the MSSNR does not require a TIR calculation, as the TIR is inherent in the way that the matrices are constructed from the channel impulse response coefficients so that the TIR is uniquely determined. In the case of additive white Gaussian noise (AWGN), the TIR is the same for both criteria, though the MSSNR is suboptimal to the MMSE in all other cases.
Although the maximization or minimization criteria in these CSF Design 144 methods vary, there are common elements to a majority of these design methods: (1) implement the CSF as a single filter that achieves the performance criterion and channel shrinking simultaneously; (2) maximize the CSF coefficients through generalized eigenvector matrix decompositions; (3) at each iteration calculate the optimum filter delay for at most L different filters, where L is the CSF Filter 142 length; and (4) calculate a TIR (in most cases).